Nonsmooth dynamics of a 3D rigid body on a vibrating plate

doi:10.1007/s11044-013-9385-4

CORC > 北京大学 > 工学院

	Nonsmooth dynamics of a 3D rigid body on a vibrating plate
	Wang, Jiao ; Liu, Caishan ; Zhao, Zhen
刊名	多体系统动力学
	2014
关键词	Nonsmooth system Multiple contact/impacts Coulomb&apos Singularity FRICTIONLESS MULTIPLE IMPACTS 3-DIMENSIONAL IMPACT MULTIBODY SYSTEMS COULOMB-FRICTION PAINLEVE PARADOX CONTACT PROBLEMS ROCKING BLOCK CONSTRAINTS RESTITUTION SIMULATION s friction
DOI	10.1007/s11044-013-9385-4
英文摘要	In this work, we study a 3D rigid body, which is in a shape similar to a dumbbell, bouncing on a harmonically vibrating plate. The system involves two contact sets whose states vary with the relative motion between the plate and the dumbbell. These states are closely related to the physical properties of contact surfaces, and can be identified using the relationships of the relative kinematics. Under certain states, system-singular modes will likely occur due to the absence of the tangential compliance in Coulomb's friction. Resolutions for these system singularities are given, and an integrated model, taking a hierarchical structure adaptable to the state variations, has been developed. Within an impact-free state, the contact forces to drive the motion of the dumbbell are obtained using an LCP (linear complementary problem) formulation. For the system in an impact state, the post-impact outputs to serve as the initial conditions for the subsequent motion can be calculated based on the new theory developed in impact dynamics. Specifying the dumbbell with initial states to bounce in a vertical plane, this model was justified by the comparison of our results and the experimental findings in other work. As certain periodic behaviors appear in the planar dynamics, the system in a 3D scenario also reveals intriguing patterns in the trajectories of the dumbbell's mass center as projected onto the horizontal plane. They include a closed circular orbit, a dog-legged path, and a straight line.; Mechanics; SCI(E); EI; 3; ARTICLE; 1001111183@pku.edu.cn; liucs@pku.edu.cn; 2; 217-239; 32
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/154232]
专题	工学院
推荐引用方式 GB/T 7714	Wang, Jiao,Liu, Caishan,Zhao, Zhen. Nonsmooth dynamics of a 3D rigid body on a vibrating plate[J]. 多体系统动力学,2014.
APA	Wang, Jiao,Liu, Caishan,&Zhao, Zhen.(2014).Nonsmooth dynamics of a 3D rigid body on a vibrating plate.多体系统动力学.
MLA	Wang, Jiao,et al."Nonsmooth dynamics of a 3D rigid body on a vibrating plate".多体系统动力学 (2014).